Question

The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for 8 hours on average. A random sample of 36 batteries was selected and placed to the test. The mean functioning time before recharge was 7.2 hours. We can assume that the population stand deviation is 1.9 hours. A competitor claims this is too high. Can you perform the appropriate test of hypothesis to determine whether the competitor is correct? Testing using alpha = 0.01

A) State and calculate the value of the test statistics

B) Use the critical value approach to test your hypothesis using alpha = 0.01

C) Use the p- value approach to test your hypothesis using alpha = 0.01. What's your conclusion?

D) Calculate an appropriate confidence interval (To sided, lower, or upper bound) and explain how it can be used to test the hypothesis.

Thanks for any help, I'm learning this stuff and it can be pretty hard!

Answer 1

A) H₀: = 8

   H₁: < 8

The test statistic z = ()/()

                            = (7.2 - 8)/(1.9/)

                            = -2.53

B) At alpha = 0.01, the critical value is z_0.99 = -2.33

Since the test statistic value is less than the critical value (-253 < -2.33), so we should reject the null hypothesis.

So at 0.01 significance level there is sufficient evidence to support the competitor's claim that 8 hours is too high.

c) P-value = P(Z < -2.53)

                  = 0.0057

Since the P-value is less than the significance level(0.0057 < 0.01), so we should reject H₀.

So at 0.01 significance level there is sufficient evidence to support the competitor's claim that 8hours is too high.

D) The upper bound 99% confidence interval is

+ z^* *

= 7.2 + 2.33 * 1.9/

= 7.2 + 0.74

= 7.94

Since the upper limit is 7.94, so we should reject the null hypothesis.